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3.1Normal(Axial)StressandStrainAxialStrain|AxialStress|Curve|Young'sModulus|Poisson'sRatio|ElasticStrainEnergy|Fatigue

AxialStrainAnaxialbaroflengthL,andcrosssectionalareaA,subjectedtotensileforceP,elongatesbyanamount,.ThechangeinlengthdividedbytheinitiallengthistermedENGINEERINGSTRAIN(orsimplystrain).Thesymbolusedforengineeringstraininmosttextsis(epsilon).Thestraininanaxiallyloadedbarisdefinedas:

Strainispositiveintension(>0means

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ValuesofEfordifferentmaterialsareobtainedexperimentallyfromstressstraincurves.Young'sModulusissimplytheslopeofthelinearregionofthestressstraincurve.ValuesofYoung'sModulusforvariousmaterialsaregiveninTable1ElasticConstants.Young'sModulusisgenerallylargeandusuallyexpressedineitherMsi(megapoundspersquareinch=thousandsofksi)orGPa(gigapascal).

StressStrainCurveThemostcommonwayofdepictingtherelationbetweenstressandstrainisthroughaSTRESSSTRAINCURVE.StressstraincurvesareobtainedexperimentallyandprovideusefulmaterialpropertiessuchasYoung'sModulus,yieldstrength,ultimatetensilestrength,etc.

Clickheretoseean

animationshowinghow

aStressStrainCurveis

constructed.

ProportionalLimit:thevalueofstresswhenthestressstraincurvenolongerfollowsHooke'sLaw.YieldStrength:thepracticalvalueoftheProportionalLimitfoundusingthe0.2%offsetrule.UltimateTensileStrength:themaximumvalueofstressthatamaterialcansupport.

Poisson'sRatioAsyoustretcharubberband,notonlydoesitelongate,butitgetsthinner.Thisholdstrueforstructuralcomponentsaswell,althoughitisdifficulttoseewiththenakedeye.ThisisreferredtoasthePoissonEffect.Mathematically,POISSON'SRATIOisexpressedasthenegativeratioofthetransversestrain(T)tothelongitudinalstrain(),wherethelongitudinalstrainisinthedirectionoftheappliedload:

TypicalvaluesofPoisson'sRatioforvariousmaterialsaregiveninTable1ElasticConstants.

ElasticStrainEnergyDensityTheelasticstrainenergydensitytheelasticstrainenergyperunitvolumestoredinanaxialmemberis:

ThemaximumvalueoftheelasticstrainenergyistheRESILIENCE.Itoccurswhenthestressintheaxialmemberreachestheyieldstrength:

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FatigueThestandardfatiguetest(zeromeanstress)hasastraintimehistorygraphasshownatright.Testsareperformedatdifferentstressamplitudesa,andthenumberofcyclestofailureisrecorded,Nf.Thepoints(NF,sa)areplottedandalinefitted.VariablesSf'andbaredeterminedfromthecurvefit.

ThefatiguestrengthofamaterialisthevalueofthestressamplitudeforagivenvalueofNfcanbecalculated:

Typically,forsteel,Nf=106cyclesandforaluminumNf=107cycles.Steelsalsohaveafatiguelimit...

Stresstimecurve.

SNCurve